Determination of incident solar radiation

Determination of incident solar radiation in Navarro's creek basin is indirect, since we extrapolate solar radiation information from sunshine hours.

Sunshine hours data is not available in the study basin, but we do have sunshine hours information in El Yeso reservoir (located 82 Km. south of Navarro's creek basin, Location map can be found here.) for the complete study period.

We transferred sunshine hours information to solar radiation through the following expression.

Where:

n: sunshine hours [hours].

N: daily mean hours of the bright sunshine [hours].

Ra: Solar extraterrestrial radiation [W/m2].

Daily mean hours of the bright sunshine is a parameter that depends on the latitude and day of the year. Its values are tabulated for a range of latitudes; we did a linear interpolation in order to adjust this parameter to Navarro's creek location.

 

Figure: Daily mean hours of bright sunshine, adjusted to Navarro's creek location.

On the other hand, solar extraterrestrial radiation it is calculated at the top of the atmosphere assuming a flat and horizontal surface. The methodology applied is the same one proposed by University of Santa Clara. (more info.)

 

 Figure: Extraterrestrial radiation Sept '07-Feb 08' adjusted to Navarro's creek basin.

Following the procedure described above, it is possible to obtain incident solar radiation distributed day by day. However, all the variables involved must be distributed both spatially and temporally.

In order to obtain a spatial distribution of the incident solar radiation, we applied a radiative gradient based on pixel elevation. (Dirección General de Aguas - Chile, 1995)

 

Finally obtained results are:

Figure: Spatially distributed incident solar radiation [W/m2] in Navarro's creek basin. To the left Sept 1st 2007, to the right October 7th 2007.

Model Implementation (1)

If precipitations inputs to the snowpack during the ablation season are small it is possible to calculate snow water equivalent (SWE) as:

Where Mj is the melt flux at time step j, SWEn is the SWE of each pixel at time step n, and SWE0 is the initial SWE or SWE at the time step corresponding to the field campaigns. By knowing any two of the three terms in the above expression the mass balance can be closed.

Research developed by Molotch and Bales raises the following mass balance for the initial snow water equivalent (SWE0)

 

Where SCA represents fractional Snow Covered Area (0-1 values) and Mvj corresponds to the daily potential maximum melt flux, which are calculated based on characteristics snow parameters (Brubaker et al, 1996).

  

 

Where:

: incoming solar radiation

: snow surface albedo (0-1 values)

: incoming thermal radiation

: outgoing thermal radiation

: energy to water depth conversion

: average daily air temperature above 0°C

: restricted degree day coefficient (0.09 cm/°C) [Brubaker et al., 1996].

Hereafter we refer to the product of Tdj and ar as turbulent transfer although it is actually a parameterization rather than an explicit calculation.

A potential melt flux (Mv) corresponds to the amount of water stored within the snowpack which potentially is available to be melted. Summation of this fluxes does not necessarily represent snowmelt runoff, since in its determination we are not including importants effects such as storage, sublimation, evaporation, etc.

This simulation is based on a reconstruction. We say reconstruction because we obtain snow water equivalent once the snow has already melted, i.e., this modeling corresponds to a post-factum estimation.

Figure: Snow accumulation/Snow melt periods representation

The snow has its own natural cycle of accumulation and melting. The accumulation period is determined by the first and last snowfall of the season, and certainly the period of melting corresponds to the inverse period. Broadly speaking in central Chile melting period starts in September and ends in February next year. The importance of a correct determination of the melting period is that the model does not consider the accumulation stage, and then any snowfall that occurs during the melting period is not being quantified in the mass balance. 

(1) Molotch, N.P., and R.C. Bales (2006), Comparison of ground-based and airbone snow surface albedo parameterizations in an alpine watershed: Impact on snowpack mass balance, Water Resour. Res., 42, W05410, doi:10.1029/2005WE004522.

Model Details

Study period corresponds to two cycles of melting period from 2007 to 2009: September 11th 2007 - February 29th 2008 and September 10th 2008 - February 28th 2009.

The main aim of this model is to perform a reconstruction of snow water equivalent day by day at a spatial scale of 500 m (0.3 miles). In order to do so, it is necessary to spatially distribute each variable involved in the simulation.

There are 7 basic variables which this model will include: (i) solar radiation, (ii) snow albedo, (iii) snow covered area, (iv) cloud coverage, (v) mean air temperature, (vi) surface snow temperature, and (vii) snow emissivity.

Snow albedo, snow covered area, cloud coverage, temperature and snow emissivity will all be acquired through satellite image information, while solar radiation and mean air temperature data will be obtained through on field measurements.

It is always important to stick to a structure or a modeling plan. I developed and followed the following methodology in order to optimize results and visualize in a better way how to proceed.

Figure: Followed methodology

   

In the next posts I will explain how I treated and modeled all the variables listed above.

Study Area

This research was performed in the upper basin of the Aconcagua river located in V region of Valparaíso in central Chile. Basin localization is delimited by 32° - 33° south latitude parallels and 71°30' - 70° west longitude meridians.

When we talk about an upper basin, we generally refer to a basin located above 1.500 msnm (about 5.000 ft); were variables such as wind, solid or liquid precipitation, temperature, incident solar radiation, etc, play a very important role in snowpack parametrization/characterization. Hence, we have chosen a mountainous sub basin as our study basin: Estero Navarro (Navarro's Creek) 

Figure: General basin localization. In red Aconcagua river basin and in blue Navarro sub basin

Navarro's sub basin is located in the upper basin of the Aconcagua river, so is characterized by a cold mountainous weather. Its average elevation reaches 3.879 masl (12.730 fasl). According to WMS 7.1 simulations, this sub basin covers an approximate area of 60,9 square kilometers (23,5 square  miles). Furthermore, it is estimated that 55% of its slopes are north-facing.

Figure: Navarro basin elevation (in meters above mean sea level, masl)

 

As you could realize, Navarro basin is located in an elevated area of Chile's Central Andes. Navarro's highest peaks are Cerro Leon Blanco 5.158 masl, Cerro Puntón amarillo 4.159 masl, and Portezuelo de Navarro 4.140 masl.

 

Figure: Navarro Basin Chart

 

Snowpack water equivalent

One of the most common properties of snowpacks needed by snow hydrologists is snowpack water equivalent. The water equivalent of a snowpack represents the liquid water that would be released upon complete melting of the snowpack.Water equivalent is measured directly or computed from measurements of depth and density of the snowpack as:

 

 

Given measurements of snowpack depth of 0.22 m and snowpack density of 256 kg m−3, the snowpack water equivalent would be:

 

   

Snowpack water equivalent includes any liquid water that may be stored in the snowpack along with the ice crystals at the time of measurement. Snowpack water equivalent is treated as a primary input to the discussion

of snow hydrology.

 

SWE can be indirectly determined trough snow density and depth. On field measurements do not measure SWE by itself, we measure snow depth and density (weight at the end) with a very rustic (?) and simple system.
   

Figure: Snow depth measurement. Farellones, Chile. ( 33.36S, 70,31W)

 

We first measure snow depth with a regular ruler, and then at a certain given snow depth we introduce a wedge. Carefully you slide a cutter at the top of the wedge and you will have a piece of snow inside this wedge (imagine it as a piece of pizza).

    

Figure: 'Wedge' inside the snowpack. Farellones, Chile

 

Figure: Snow perfectly cut and fit into the 'wedge' . Farellones, Chile.

 

Since the 'wedge' mass is known, weighting it you will have snow mass. Wedge volume it is also known (250cc or 1000cc), thus you can determine snow density at that given depth. Then with the snowdepth you can estimate Snow Water Equivalent.

Principles of snow hydrology

Snow hydrology is a specialized field of hydrology that is of particular importance for high latitudes and mountainous terrain. In many parts of the world, river and groundwater supplies for domestic, irrigation, industrial, and ecosystem needs are generated from snowmelt, and an in-depth understanding of snow hydrology is of clear importance. Study of the impacts of global warming has also stimulated interest in snow hydrology because increased air temperatures are projected to have major impacts on the snow hydrology of cold regions.
 
Snow Hydrology describes the factors that control the accumulation, melting, and runoff of water from seasonal snowpacks over the surface of the earth. This research field addresses not only the basic principles governing snow in the hydrologic cycle, but also the latest applications of remote sensing, and principles applicable to modeling streamflow from snowmelt across large, mixed land use river basins.

 

Figure: Estero Monos de Agua Basin. Central Andes, Chile

Although history suggests that technical understanding of snow hydrology was a relatively recent phenomenon, some evidence exists that the role of snow was understood by some very early in our study of the physical world. References to the philosophy of the ancient Greek, Anaxagoras (500–428 BCE), indicate a rather surprising early understanding of the relationships between river flows and freezing and thawing of water, for example (Franks 1898): “The Nile comes from the snow in Ethiopia which melts in summer and freezes in winter” (Aet. Plac. iv 1;385); “And the Nile increases in summer because waters flow down into it from snows at the north” (Hipp. Phil. 8; Dox. 561). 


Much later, literature from the writings of naturalist/geologist AntonioVallisnieri (1661–1730) in Italy showed specific recognition of the role of snow in hydrology. He correctly theorized that rivers arising from springs in the Italian Alps came from rain and snowmelt seeping into underground channels.

In the United States during World War II, the US Army Corps of Engineers and the USWeather Bureau initiated the Cooperative Snow Investigations in 1944 (US ArmyCorps of Engineers, 1956). The snow investigations were organized to address specific snow hydrology problems that were being encountered by both agencies. In order to meet snow hydrology objectives of both agencies, it was deemed necessary to establish fundamental research in the physics of snow. An extensive laboratory program across the western United States was established and observations were gathered starting in 1945. Analysis of these data formed the basis for developing the basic relationships and methods of application derived to develop solutions to the key snow hydrology problems (US Army Corps of Engineers, 1956).

Figure: Instrumentation at the Central Sierra Snow Laboratory in Soda Springs, CA. United States